Group #13131048 — subgroups

Subgroups — #13131048

Order 1664.

184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11719089	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	D₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
4	#11718216	C₂	1	2	yes	maximal, complemented
5	C₁₆×#261	C₂	1	2	yes	maximal, complemented
6	#88237	C₄	1	1	yes	characteristic
7	D₁₃⋊M₁₆	C₄	1	1	yes	characteristic
8	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×#6092	C₄	1	2	yes	complemented
10	#88100	C₄	1	2	yes	—
11	C₈×#261	C₂²	1	2	yes	—
12	D₁₃⋊C₁₆	C₄	1	2	yes	complemented
13	D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
14	D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₁₃×M₃₂	C₄	1	1	yes	characteristic, complemented
16	#88052	C₄	1	1	yes	characteristic, complemented
17	#88038	C₄	1	2	yes	complemented
18	C₁₆×D₁₃	C₂²	1	2	yes	—
19	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²⋊#261	C₈	1	2	yes	—
21	#6122	C₈	1	2	yes	—
22	C₄⋊#261	C₈	1	2	yes	—
23	C₄×#261	C₂×C₄	1	2	yes	—
24	#6118	C₈	1	2	yes	—
25	D₁₃⋊C₈	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×#1055	C₂×C₄	1	1	yes	characteristic
28	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
30	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
31	C₈×D₁₃	C₂³	1	1	yes	characteristic
32	#6092	C₂×C₄	1	2	yes	—
33	#6092	C₂×C₄	1	2	yes	—
34	C₁₃×C₁₆	C₂×C₄	1	2	yes	—
35	#6090	C₂×C₄	1	2	yes	—
36	#2108	—	13	1	no	maximal, Sylow
37	C₂²×D₁₃	C₂×C₈	1	1	yes	characteristic
38	C₂×#261	C₂×C₈	1	4	yes	—
39	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
40	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
41	C₄×D₁₃	C₄²	1	1	yes	characteristic
42	C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
43	C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
44	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
45	#1057	C₂×C₈	1	4	yes	—
46	C₈×C₁₃	C₄²	1	1	yes	characteristic
47	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	#1055	C₄²	1	1	yes	characteristic
49	#1055	C₂²×C₄	1	1	yes	characteristic
50	C₂×M₃₂	—	13	1	no	—
51	C₂²×C₁₆	—	13	1	no	—
52	#405	—	13	1	no	—
53	#346	—	13	2	no	—
54	C₄×C₁₆	—	13	2	no	—
55	C₂²×C₁₃	C₄×C₈	1	1	yes	characteristic
56	C₂×D₁₃	—	2	2	no	—
57	C₂×D₁₃	C₄×C₈	1	1	yes	characteristic
58	C₂×D₁₃	C₂²×C₈	1	1	yes	characteristic
59	#261	—	2	4	no	—
60	C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
61	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
62	Dic₁₃	C₄×C₈	1	1	yes	characteristic
63	Dic₁₃	C₂²×C₈	1	1	yes	characteristic
64	C₂×M₁₆	—	13	1	no	—
65	C₂²×C₈	—	13	1	no	—
66	#117	—	13	1	no	—
67	M₃₂	—	13	1	no	—
68	M₃₂	—	13	2	no	—
69	M₃₂	#261	1	1	yes	characteristic, complemented
70	C₂×C₁₆	—	13	2	no	—
71	C₂×C₁₆	—	13	1	no	—
72	C₂×C₁₆	—	13	1	no	—
73	C₂×C₁₆	—	13	2	no	—
74	C₂×C₁₆	—	13	2	no	—
75	#97	—	13	2	no	—
76	C₄×C₈	—	13	2	no	—
77	C₂×C₁₃	—	2	1	no	—
78	C₂×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
79	D₁₃	—	2	1	no	—
80	D₁₃	#504	1	2	yes	—
81	C₂²×C₄	—	13	1	no	—
82	M₁₆	—	13	2	no	—
83	M₁₆	—	13	2	no	—
84	C₂×C₈	—	13	2	no	—
85	C₂×C₈	—	13	1	no	—
86	C₂×C₈	—	13	1	no	—
87	C₂×C₈	—	13	1	no	—
88	C₂×C₈	—	13	1	no	—
89	C₂×C₈	—	13	1	no	—
90	C₂×C₈	C₂×#261	1	1	yes	characteristic
91	C₄⋊C₄	—	13	2	no	—
92	C₂²⋊C₄	—	13	2	no	—
93	C₄²	—	13	2	no	—
94	C₁₆	—	13	2	no	—
95	C₁₆	—	13	2	no	—
96	C₁₆	—	13	2	no	—
97	C₁₆	C₂×#261	1	2	yes	—
98	C₁₃	#2108	1	1	yes	characteristic, complemented, Sylow
99	C₂³	—	13	1	no	—
100	C₂×C₄	—	13	1	no	—
101	C₂×C₄	—	13	1	no	—
102	C₂×C₄	—	13	1	no	—
103	C₂×C₄	—	13	1	no	—
104	C₂×C₄	—	13	1	no	—
105	C₂×C₄	—	13	4	no	—
106	C₂×C₄	C₄×#261	1	1	yes	characteristic
107	C₈	—	13	4	no	—
108	C₈	—	13	1	no	—
109	C₈	—	13	1	no	—
110	C₈	C₄×#261	1	1	yes	characteristic
111	C₈	C₂²×#261	1	1	yes	characteristic
112	C₂²	—	13	1	no	—
113	C₂²	—	13	1	no	—
114	C₂²	—	26	2	no	—
115	C₂²	C₈×#261	1	1	yes	characteristic
116	C₄	—	13	1	no	—
117	C₄	—	13	1	no	—
118	C₄	—	26	4	no	—
119	C₄	C₈×#261	1	1	yes	characteristic
120	C₄	C₂×C₄×#261	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	13	2	no	—
123	C₂	—	26	1	no	—
124	C₂	C₂×C₈×#261	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11719089

C₂

yes

maximal, characteristic

C₂×D₁₃⋊C₁₆

C₂

yes

maximal, characteristic

D₁₃×M₃₂

C₂

yes

maximal, characteristic

#11718216

C₂

yes

maximal, complemented

C₁₆×#261

C₂

yes

maximal, complemented

#88237

C₄

yes

characteristic

D₁₃⋊M₁₆

C₄

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₂×#6092

C₄

yes

complemented

#88100

C₄

yes

—

C₈×#261

C₂²

yes

—

D₁₃⋊C₁₆

C₄

yes

complemented

D₁₃⋊C₁₆

C₂²

yes

characteristic

D₁₃⋊C₁₆

C₂²

yes

characteristic

C₁₃×M₃₂

C₄

yes

characteristic, complemented

#88052

C₄

yes

characteristic, complemented

#88038

C₄

yes

complemented

C₁₆×D₁₃

C₂²

yes

—

C₂×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂²⋊#261

C₈

yes

—

#6122

C₈

yes

—

C₄⋊#261

C₈

yes

—

C₄×#261

C₂×C₄

yes

—

#6118

C₈

yes

—

D₁₃⋊C₈

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×#1055

C₂×C₄

yes

characteristic

C₈×D₁₃

C₂×C₄

yes

characteristic

C₈×D₁₃

C₂×C₄

yes

characteristic

C₈×D₁₃

C₂×C₄

yes

characteristic

C₈×D₁₃

C₂³

yes

characteristic

#6092

C₂×C₄

yes

—

#6092

C₂×C₄

yes

—

C₁₃×C₁₆

C₂×C₄

yes

—

#6090

C₂×C₄

yes

—

#2108

—

maximal, Sylow

C₂²×D₁₃

C₂×C₈

yes

characteristic

C₂×#261

C₂×C₈

yes

—

C₂×C₄×C₁₃

C₄²

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₄×D₁₃

C₄²

yes

characteristic

C₄×D₁₃

C₂×C₈

yes

characteristic

C₄×D₁₃

C₂×C₈

yes

characteristic

C₄×D₁₃

C₂²×C₄

yes

characteristic

#1057

C₂×C₈

yes

—

C₈×C₁₃

C₄²

yes

characteristic

C₈×C₁₃

C₂²×C₄

yes

characteristic

#1055

C₄²

yes

characteristic

#1055

C₂²×C₄

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

C₄×C₁₆

—

C₂²×C₁₃

C₄×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₄×C₈

yes

characteristic

C₂×D₁₃

C₂²×C₈

yes

characteristic

#261

—

C₄×C₁₃

C₄×C₈

yes

characteristic

C₄×C₁₃

C₂×C₄²

yes

characteristic

Dic₁₃

C₄×C₈

yes

characteristic

Dic₁₃

C₂²×C₈

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

#261

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

C₂×C₄×C₈

yes

characteristic

D₁₃

—

D₁₃

#504

yes

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#261

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

C₂×#261

yes

—

C₁₃

#2108

yes

characteristic, complemented, Sylow

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₄×#261

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

C₄×#261

yes

characteristic

111

C₈

C₂²×#261

yes

characteristic

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₈×#261

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

C₈×#261

yes

characteristic

120

C₄

C₂×C₄×#261

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

124

C₂

C₂×C₈×#261

yes

characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#261
commutator, socle	C₂×C₁₃	C₂×C₄×C₈
Fitting	C₁₃×M₃₂	C₄
prime radical	C₂²×D₁₃	C₂×C₈
cosocle	C₈×D₁₃	C₂³
hypercenter	M₃₂	#261
hypocenter	C₁₃	#2108
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ M₃₂

subgroup

G/H

center, Frattini

C₈

C₂²×#261

commutator, socle

C₂×C₁₃

C₂×C₄×C₈

Fitting

C₁₃×M₃₂

C₄

prime radical

C₂²×D₁₃

C₂×C₈

cosocle

C₈×D₁₃

C₂³

M₃₂

C₁₃

G ▷ C₂×C₁₃ ▷ C₁₃

C₁ ◁ C₈ ◁ M₃₂

N	H ≅ G/N	type
4. #11718216	C₂	semidirect
5. C₁₆×#261	C₂	semidirect
9. C₂×#6092	C₄	semidirect
12. D₁₃⋊C₁₆	C₄	semidirect
15. C₁₃×M₃₂	C₄	semidirect
16. #88052	C₄	semidirect
17. #88038	C₄	semidirect
69. M₃₂	#261	semidirect
98. C₁₃	#2108	semidirect

H ≅ G/N

type

4. #11718216

C₂

semidirect

5. C₁₆×#261

C₂

semidirect

9. C₂×#6092

C₄

semidirect

12. D₁₃⋊C₁₆

C₄

semidirect

15. C₁₃×M₃₂

C₄

semidirect

16. #88052

C₄

semidirect

17. #88038

C₄

semidirect

69. M₃₂

#261

semidirect

98. C₁₃

#2108

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11719089	2
C₂×D₁₃⋊C₁₆	2
D₁₃×M₃₂	2
#11718216	2
C₁₆×#261	2
#2108	13

subgroup

index

#11719089

C₂×D₁₃⋊C₁₆

D₁₃×M₃₂

#11718216

C₁₆×#261

#2108

Subgroups — #13131048

Conjugacy classes of subgroups

Complements

Maximal subgroups